Peng Zhou 周鹏 - Research

Research Interests

I am interested in mathematical physics, geometric representation theory and symplectic geometry. I have done research in homological mirror symmetry (HMS) for toric varieties, microlocal sheaf-theoretic symplectic geometry, log D-modules. I also worked on microlocal analysis, for example solving Schoedinger equations when h -> 0, or high powers of ample line bundles.

Currently, I am working on a few HMS problems, one is about categorification of knot invariants, one is about type $A_n$ cluster varieties, another is about complete intersections in $(\C^*)^n$. I am also interested in relating wall-crossing phenomenon in HMS.

You can see my most up to date publications in Google Scholar, which include past publications from physics. Here is a cleaned up list about math.

Publications

12. Jesse Huang and Peng Zhou. Variation of GIT and variation of Lagrangian skeletons II: Quasi-symmetric case. Advances in Mathematics, 408:108597, 2022

11. Nero Budur, Robin van der Veer, Lei Wu, and Peng Zhou. Zero loci of Bernstein-Sato ideals-II. Selecta Mathematica, 27(3):1–30, 2021

10. Nero Budur, Robin van der Veer, Lei Wu, and Peng Zhou. Zero loci of Bernstein–Sato ideals. Inventiones mathematicae, 225(1):45–72, 2021

9. Lei Wu and Peng Zhou. Log-modules and index theorems. In Forum of Mathematics, Sigma, volume 9. Cambridge University Press, 2021

8. Peng Zhou. Lagrangian skeleta of hypersurfaces in (C∗)n. Selecta Math- ematica, 26:26, 2020

7. Peng Zhou. Twisted polytope sheaves and coherent–constructible corre- spondence for toric varieties. Selecta Mathematica, 25(1):1, 2019

6. Steve Zelditch and Peng Zhou. Interface asymptotics of partial Bergman kernels around a critical level. Arkiv f ̈or Matematik, 57(2):471–492, 2019

5. Steve Zelditch and Peng Zhou. Central limit theorem for spectral partial Bergman kernels. Geometry & Topology, 23(4):1961–2004, 2019

4. Steve Zelditch and Peng Zhou. Interface asymptotics of partial Bergman kernels on S1-symmetric K ̈ahler manifolds. Journal of Symplectic Geom- etry, 17(3):793–856, 2019

3. Steve Zelditch and Peng Zhou. Pointwise Weyl Law for Partial Bergman Kernels. Algebraic and Analytic Microlocal Analysis, page 589, 2018

2. Boris Hanin, Steve Zelditch, and Peng Zhou. Scaling of harmonic oscillator eigenfunctions and their nodal sets around the caustic. Communications in Mathematical Physics, 350(3):1147–1183, 2017

1. Boris Hanin, Steve Zelditch, and Peng Zhou. Nodal sets of random eigenfunctions for the isotropic harmonic oscillator. International Mathematics Research Notices, 2015(13):4813–4839, 2015

Preprints

4. Jesse Huang and Peng Zhou. GKZ discriminant and Multiplicities. arXiv preprint arXiv:2206.14778, 2022

3. Peng Zhou. Variation of GIT and variation of Lagrangian skeletons I: flip and flop. arXiv preprint arXiv:2011.03719, 2020

2. Bohan Fang and Peng Zhou. Gamma II for toric varieties from inte- grals on T-dual branes and homological mirror symmetry. arXiv preprint arXiv:1903.05300, 2019

1. Peng Zhou. Sheaf Quantization of Legendrian Isotopy. arXiv preprint arXiv:1804.08928, 2018